library(rstan)
Loading required package: StanHeaders
Loading required package: ggplot2
rstan (Version 2.21.1, GitRev: 2e1f913d3ca3)
For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores()).
To avoid recompilation of unchanged Stan programs, we recommend calling
rstan_options(auto_write = TRUE)
library(survival)
library(tidyverse)
Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
── Attaching packages ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.1 ──
✓ tibble 3.1.4 ✓ dplyr 1.0.7
✓ tidyr 1.1.3 ✓ stringr 1.4.0
✓ readr 2.0.1 ✓ forcats 0.5.1
✓ purrr 0.3.4
── Conflicts ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
x tidyr::extract() masks rstan::extract()
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()
library(tidybayes)
library(scales)
Attaching package: ‘scales’
The following object is masked from ‘package:purrr’:
discard
The following object is masked from ‘package:readr’:
col_factor
library(survminer)
Loading required package: ggpubr
Registered S3 method overwritten by 'data.table':
method from
print.data.table
# data, parameters, model and generated quantities blocks
Stan_exponential_survival_model <- "
data{
int <lower=1> N_uncensored;
int <lower=1> N_censored;
int <lower=0> numCovariates;
matrix[N_censored, numCovariates] X_censored;
matrix[N_uncensored, numCovariates] X_uncensored;
vector <lower=0>[N_censored] times_censored;
vector <lower=0>[N_uncensored] times_uncensored;
}
parameters{
vector[numCovariates] beta; //regression coefficients
real alpha; //intercept
}
model{
beta ~ normal(0,10); //prior on regression coefficients
alpha ~ normal(0,10); //prior on intercept
target += exponential_lpdf(times_uncensored | exp(alpha+X_uncensored * beta)); //log-likelihood part for uncensored times
target += exponential_lccdf(times_censored | exp(alpha+X_censored * beta)); //log-likelihood for censored times
}
generated quantities{
vector[N_uncensored] times_uncensored_sampled; //prediction of death
for(i in 1:N_uncensored) {
times_uncensored_sampled[i] = exponential_rng(exp(alpha+X_uncensored[i,]* beta));
}
}
"
# prepare the data
set.seed(42);
require (tidyverse);
data <- read_csv('../data/necessary_fields.csv')
Rows: 2066 Columns: 7
── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): host_type
dbl (1): duration_months
lgl (5): major_releases, censored, high_rev_freq, multi_repo, high_author_count
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
N <- nrow (data);
data$multi_repo <- car::recode(data$multi_repo, "'TRUE' = 0; 'FALSE' = 1")
data$censored <- car::recode(data$censored, "'TRUE' = 0; 'FALSE' = 1")
X <- as.matrix(pull(data, multi_repo));
is_censored <- pull(data, censored)==0;
times <- pull(data, duration_months);
msk_censored <- is_censored == 1;
N_censored <- sum(msk_censored);
# put data into a list for Stan
Stan_data <- list (N_uncensored = N - N_censored,
N_censored = N_censored,
numCovariates = ncol(X),
X_censored = as.matrix(X[msk_censored,]),
X_uncensored = as.matrix(X[!msk_censored ,]),
times_censored = times[msk_censored],
times_uncensored = times[!msk_censored])
# fit Stan model
require(rstan)
exp_surv_model_fit <- suppressMessages(stan(model_code = Stan_exponential_survival_model, data = Stan_data))
sh: Data/bayesian: No such file or directory
Warning in system2(CXX, args = ARGS) : error in running command
Warning in file.remove(c(unprocessed, processed)) :
cannot remove file '/var/folders/q8/7tchbyvd1dj3hkgw5ffkk6ph0000gp/T//RtmpKsHNQc/file9c702b7c6dec.stan', reason 'No such file or directory'
sh: clang++ -mmacosx-version-min=10.13: command not found
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.000481 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 4.81 seconds.
Chain 1: Adjust your expectations accordingly!
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Chain 1:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 2).
Chain 2:
Chain 2: Gradient evaluation took 0.000196 seconds
Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 1.96 seconds.
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Chain 2:
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Chain 2:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 3).
Chain 3:
Chain 3: Gradient evaluation took 0.000203 seconds
Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 2.03 seconds.
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Chain 3:
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 4).
Chain 4:
Chain 4: Gradient evaluation took 0.000195 seconds
Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 1.95 seconds.
Chain 4: Adjust your expectations accordingly!
Chain 4:
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# print model fit
print(get_seed(exp_surv_model_fit))
[1] 1781592037
# print fit summary
fit_summary <- summary(exp_surv_model_fit)
print(fit_summary$summary)
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
beta[1] 1.237474 0.007908949 0.2184724 0.8278381 1.092083 1.229948 1.374603 1.687030 763.0548 1.0006992
alpha -5.998177 0.007768561 0.2152980 -6.4454373 -6.138731 -5.990108 -5.854118 -5.587744 768.0666 1.0006953
times_uncensored_sampled[1] 114.563520 1.837459182 114.0407784 2.4568818 31.892139 79.240041 161.134308 417.622660 3851.9882 1.0007646
times_uncensored_sampled[2] 115.644401 1.824486836 114.8785914 3.0066199 34.650552 81.793933 159.445637 429.419951 3964.5759 1.0003087
times_uncensored_sampled[3] 116.819410 1.842932854 113.8019114 3.5796150 35.062306 83.334274 160.085429 438.103136 3813.1166 0.9993520
times_uncensored_sampled[4] 119.436497 1.884441829 120.0833701 3.0544884 33.863453 81.209952 164.857425 442.464711 4060.6940 1.0002426
times_uncensored_sampled[5] 117.891291 1.817152486 116.7332958 3.7771450 33.809990 80.814402 166.268726 436.095921 4126.7366 1.0006293
times_uncensored_sampled[6] 116.994273 1.898037634 118.9686408 2.7500939 33.048916 80.898408 161.612631 444.910007 3928.7587 1.0001449
times_uncensored_sampled[7] 117.642811 1.869465177 116.1300834 3.1787506 34.571120 82.758131 165.274436 422.580337 3858.8217 1.0004184
times_uncensored_sampled[8] 115.178674 1.772909730 114.7357260 3.1337112 32.450490 79.773488 161.266041 412.390758 4188.1679 1.0004307
times_uncensored_sampled[9] 116.330523 1.947957209 117.2093441 2.5507989 33.348408 80.765037 160.234529 428.850406 3620.4758 0.9995617
times_uncensored_sampled[10] 115.790518 1.807664746 115.0930266 2.8692665 33.800092 80.321039 161.776534 423.529276 4053.7993 0.9996944
times_uncensored_sampled[11] 117.596197 1.837352799 116.7778888 2.8208116 33.689348 82.780866 161.873819 430.216108 4039.5792 0.9997525
times_uncensored_sampled[12] 115.194094 1.804527647 115.2445760 2.7235515 32.542163 79.188164 161.477446 426.862284 4078.6262 1.0005661
times_uncensored_sampled[13] 116.732502 1.839843284 115.4392163 3.0360671 35.188911 82.101549 162.036819 418.718626 3936.8156 0.9997012
times_uncensored_sampled[14] 120.484399 1.932144909 122.1088624 2.8011592 32.853501 81.553801 171.038773 439.683274 3994.0636 0.9999205
times_uncensored_sampled[15] 117.403060 1.924548124 120.1508774 3.3964327 32.913646 78.768683 160.163404 445.568811 3897.5917 0.9995690
times_uncensored_sampled[16] 116.369742 1.802165029 113.4495087 3.5083646 34.033509 78.701440 165.202254 416.545608 3962.9275 1.0000141
times_uncensored_sampled[17] 116.525019 1.895350812 116.4297149 2.4801724 34.114123 81.348031 159.156231 424.726445 3773.5356 0.9998803
times_uncensored_sampled[18] 119.044333 1.980047633 118.0862989 2.8090583 34.250687 81.359318 166.654472 444.460092 3556.7042 1.0007019
times_uncensored_sampled[19] 117.400332 1.991495531 118.5693667 3.1160080 33.366716 79.043252 162.056659 439.376097 3544.7559 1.0008059
times_uncensored_sampled[20] 117.810152 1.872014546 119.2956470 2.6207819 33.996288 81.347571 164.458612 425.105602 4060.9791 0.9998185
times_uncensored_sampled[21] 118.554440 1.927248799 117.8609877 2.9556187 34.316002 82.482623 163.798112 435.011340 3739.9396 0.9997950
times_uncensored_sampled[22] 118.974024 1.874065446 119.4651380 2.6225398 34.036153 81.736563 165.920045 445.871203 4063.6180 0.9993442
times_uncensored_sampled[23] 112.874179 1.946434626 110.5213808 2.9174608 33.069418 78.921806 157.450987 420.929850 3224.1331 1.0004010
times_uncensored_sampled[24] 412.535952 7.538444523 437.3392704 8.8759851 111.343655 277.214774 560.050792 1534.868300 3365.6850 0.9998746
times_uncensored_sampled[25] 122.224853 1.865218120 121.4751825 2.8493874 35.925866 84.719405 174.068793 441.735914 4241.4648 0.9997263
times_uncensored_sampled[26] 120.101841 1.906880036 118.2023972 3.5108834 34.402372 85.264381 165.074265 436.611712 3842.4288 0.9992165
times_uncensored_sampled[27] 120.008485 1.988773583 121.9260060 3.0607592 34.211453 82.206197 162.064643 461.123365 3758.5645 1.0003699
times_uncensored_sampled[28] 115.479381 1.835497692 115.8867913 2.5151007 32.290426 79.871596 161.424153 417.874353 3986.2102 0.9997327
times_uncensored_sampled[29] 117.031797 1.888034853 118.5345351 2.9538814 34.661931 80.570718 161.682045 440.602873 3941.5749 0.9998649
times_uncensored_sampled[30] 115.314226 1.898743040 118.9851846 2.9359084 31.066262 76.351228 160.507405 432.812460 3926.9321 0.9997087
times_uncensored_sampled[31] 117.638162 2.004749081 122.1925394 3.1820807 32.814989 78.228938 161.525429 450.702140 3715.0900 0.9995991
times_uncensored_sampled[32] 117.138188 1.870751662 115.4297883 2.9815895 33.253829 82.334081 162.271021 432.722015 3807.1810 0.9997263
times_uncensored_sampled[33] 115.717401 1.869458231 113.9879092 3.0644653 33.419130 81.314320 163.825196 413.254806 3717.8002 1.0001079
times_uncensored_sampled[34] 120.008500 1.905909502 121.3622074 3.2532771 34.987746 84.580338 164.115599 429.851116 4054.7341 1.0000852
times_uncensored_sampled[35] 116.750810 1.837259559 116.3287138 3.1440953 33.006976 81.980091 162.169939 440.512405 4008.9701 1.0005699
times_uncensored_sampled[36] 117.490932 1.867983649 115.7511571 2.7508074 34.075965 81.559165 164.176301 424.451641 3839.7641 1.0010271
times_uncensored_sampled[37] 116.315164 1.879284234 118.8415098 3.1796313 32.286362 79.199806 162.545072 424.633358 3998.9998 0.9993207
times_uncensored_sampled[38] 116.307542 1.911654730 117.5921404 2.6258308 33.810689 79.021481 159.201416 434.790855 3783.8828 0.9998369
times_uncensored_sampled[39] 117.330894 2.038261433 115.8941385 2.8272365 33.305807 81.343545 165.269990 411.787547 3232.9811 1.0000191
times_uncensored_sampled[40] 113.440341 1.885845145 117.1806116 2.7528183 31.144236 77.288693 156.465217 444.661049 3860.9970 0.9997371
times_uncensored_sampled[41] 115.769893 1.729463859 111.4090935 3.3448325 32.687791 81.545298 164.756267 415.994483 4149.7153 0.9996285
times_uncensored_sampled[42] 117.813343 1.848612534 116.1864425 2.9039792 34.922921 82.028088 161.709660 426.265195 3950.2003 0.9999293
times_uncensored_sampled[43] 118.255772 1.947199549 118.1612646 3.7630707 33.311039 80.860933 164.336246 431.090969 3682.3862 1.0012290
times_uncensored_sampled[44] 117.292285 1.908341917 119.0940559 2.9862616 34.415958 81.277258 157.435925 439.437872 3894.6442 1.0006046
times_uncensored_sampled[45] 118.649344 1.898512651 119.2687297 3.1068938 34.151504 83.060229 162.862096 427.838978 3946.6280 0.9998051
times_uncensored_sampled[46] 115.365830 1.876617919 114.6354073 3.0379727 33.651592 79.644413 159.166936 413.317493 3731.5206 0.9995702
times_uncensored_sampled[47] 115.529657 1.889105491 114.9938524 2.5788932 34.245325 78.746230 161.103656 428.182942 3705.4147 0.9994047
times_uncensored_sampled[48] 114.389154 1.893868434 118.2190185 3.1155235 32.191944 78.690477 156.914497 433.289514 3896.5037 0.9993100
times_uncensored_sampled[49] 116.734025 1.862236654 112.9391220 2.7846205 33.515822 83.759398 162.486539 417.845663 3678.0622 0.9997950
times_uncensored_sampled[50] 116.494561 1.868064152 118.4261878 2.9034874 31.797247 78.981033 161.876063 443.160527 4018.9437 0.9997018
times_uncensored_sampled[51] 116.783831 1.877234552 116.8204766 2.5847164 33.962558 81.272447 162.028854 430.925734 3872.5842 0.9998843
times_uncensored_sampled[52] 116.434195 1.805444549 113.1539634 3.1457660 34.038188 80.448871 163.217093 412.727745 3927.9978 0.9996780
times_uncensored_sampled[53] 123.832003 1.943816408 122.8065188 3.1345705 35.446753 85.059660 172.885103 459.750971 3991.4653 0.9997243
times_uncensored_sampled[54] 116.219361 1.829368154 113.7842417 2.9034064 34.720874 79.349423 163.913418 422.544673 3868.6729 0.9992595
times_uncensored_sampled[55] 115.001415 1.791344146 113.6660926 2.9178405 34.365971 81.236770 158.089230 414.184198 4026.2784 0.9999097
times_uncensored_sampled[56] 115.112713 1.892069439 114.6985686 3.0249014 32.716065 78.473881 159.588126 436.220531 3674.8689 1.0001461
times_uncensored_sampled[57] 115.016108 1.865289093 115.2950040 2.7582524 31.622085 80.395632 160.785592 419.949710 3820.5745 1.0007811
times_uncensored_sampled[58] 115.792372 1.862052684 115.4349216 3.3789523 34.063507 80.477616 158.535325 431.965162 3843.1780 0.9999365
times_uncensored_sampled[59] 116.665262 1.913401316 119.2563448 2.8560893 32.996410 80.561082 160.374985 445.219239 3884.6407 0.9996020
times_uncensored_sampled[60] 115.887370 1.798642670 116.0210876 3.2422545 33.354128 80.279383 156.772636 420.035207 4160.8694 1.0005379
times_uncensored_sampled[61] 119.368524 1.927472043 119.5896981 3.2185836 34.809389 82.310272 167.905618 436.969271 3849.5624 1.0003193
times_uncensored_sampled[62] 118.030807 1.894313127 116.7588967 2.5281294 33.538741 82.327326 165.377599 414.794693 3799.0624 1.0007484
times_uncensored_sampled[63] 118.750642 1.876850014 118.8846170 3.1421360 33.881112 82.421983 161.918312 427.132127 4012.2888 0.9998191
times_uncensored_sampled[64] 112.714862 1.850772502 119.5454497 2.3096143 30.208798 74.551735 154.363131 448.141258 4172.1511 0.9994665
times_uncensored_sampled[65] 114.833955 1.865581917 116.8287301 3.2116885 33.135417 77.448960 161.083267 424.595457 3921.6666 1.0004827
times_uncensored_sampled[66] 120.709803 1.863691966 120.3623805 3.1975269 34.606598 84.126169 166.847803 442.063917 4170.9335 1.0001504
times_uncensored_sampled[67] 117.608570 1.850573651 118.0277614 2.6612538 32.350371 82.800411 164.455008 431.418447 4067.7625 0.9997873
times_uncensored_sampled[68] 116.439320 1.807300836 117.8952067 2.7461112 32.597916 79.356567 162.856349 432.226396 4255.3119 0.9996318
times_uncensored_sampled[69] 117.117251 1.917045288 119.0928814 2.6431777 33.015902 79.121966 162.665533 427.898552 3859.2851 1.0000418
times_uncensored_sampled[70] 119.574233 1.918985482 118.1748250 2.9884185 34.976773 82.913042 168.390967 429.680146 3792.3338 0.9991319
times_uncensored_sampled[71] 116.605720 1.906257779 119.2862296 2.7526822 33.302700 76.729040 161.865513 437.952770 3915.7717 1.0000881
times_uncensored_sampled[72] 115.509036 1.955351817 123.1091810 2.4017121 32.660218 78.658996 156.277202 442.198192 3963.9765 1.0000233
times_uncensored_sampled[73] 113.145579 1.863083493 114.8336712 3.1178683 31.127114 79.076104 157.029957 406.780334 3799.0400 1.0008255
times_uncensored_sampled[74] 116.571755 1.865331676 116.0904974 2.5603608 34.657257 78.990652 163.432567 433.393119 3873.3007 1.0001140
times_uncensored_sampled[75] 117.312164 1.877487842 114.8107333 2.6538158 33.547124 82.544603 165.028549 419.693848 3739.4757 1.0003857
times_uncensored_sampled[76] 115.911359 1.869481071 115.9818912 3.3614961 34.878681 79.253067 158.301583 425.638227 3848.9142 1.0011785
times_uncensored_sampled[77] 120.009590 1.895298767 117.5454427 2.8654953 34.633717 85.100487 168.210187 439.068696 3846.4158 1.0008081
times_uncensored_sampled[78] 118.500651 1.874885470 117.9023659 3.2866989 34.819864 80.924121 163.945429 440.115184 3954.5362 1.0009745
times_uncensored_sampled[79] 119.614612 2.020632684 122.6015678 2.8559348 34.526590 84.059916 162.369025 445.900877 3681.4364 1.0001408
times_uncensored_sampled[80] 113.905370 1.844540633 115.6216388 3.1838905 33.543140 78.666561 159.872830 415.453297 3929.1788 1.0000333
times_uncensored_sampled[81] 117.753559 1.853328060 117.0974099 2.6908536 34.871810 79.696405 162.235825 443.008500 3991.9949 1.0000064
times_uncensored_sampled[82] 115.703053 2.013782885 115.7796032 2.6256264 32.994229 80.446445 163.457570 425.574418 3305.5126 1.0004408
times_uncensored_sampled[83] 119.260615 1.852948058 120.3237606 2.7645064 34.279221 81.230812 165.135477 449.495711 4216.7349 1.0010982
times_uncensored_sampled[84] 116.102750 1.803915927 114.9241674 3.5769031 34.250719 80.938078 162.146585 419.588211 4058.7299 1.0000843
times_uncensored_sampled[85] 117.128847 1.870386431 116.5782726 3.4428239 32.725839 80.535864 163.054385 438.232988 3884.8347 0.9996910
times_uncensored_sampled[86] 116.658181 1.866241569 117.3398034 2.9689830 32.707535 79.822101 162.119750 436.114860 3953.2565 1.0000681
times_uncensored_sampled[87] 115.771211 1.821585559 115.8509865 3.2812594 32.709645 79.642455 160.142693 428.324817 4044.8305 0.9996226
times_uncensored_sampled[88] 116.983857 1.854787396 116.9207721 3.3877242 34.109489 80.678860 164.119449 435.477492 3973.7000 1.0001547
times_uncensored_sampled[89] 118.521314 1.886370168 119.4089176 3.1499202 34.086960 82.342311 162.202195 440.885839 4007.0032 0.9997752
times_uncensored_sampled[90] 117.759313 1.851909929 116.1639029 2.9147852 34.861812 83.094948 165.388242 426.890184 3934.6189 0.9996183
times_uncensored_sampled[91] 114.943629 1.820470956 114.3465664 3.0005340 33.639162 81.027187 159.718043 425.806096 3945.2883 0.9990669
times_uncensored_sampled[92] 117.865918 1.934206852 118.6019196 2.2970831 32.863038 82.113594 164.478941 435.248376 3759.9113 1.0000991
times_uncensored_sampled[93] 115.718864 1.885305543 119.1521793 2.4855951 31.825874 78.107677 155.257531 436.486745 3994.2983 0.9998687
times_uncensored_sampled[94] 113.741959 1.708122522 109.6807791 2.3645031 34.269941 79.934860 160.234520 410.682726 4123.0919 1.0009693
times_uncensored_sampled[95] 117.662357 1.879326857 119.3114186 3.1481477 33.887090 78.611047 163.444833 445.947579 4030.5042 0.9995995
times_uncensored_sampled[96] 117.101244 1.852471606 115.9192904 2.9521098 34.046265 81.762770 162.968288 418.686646 3915.6901 1.0003979
times_uncensored_sampled[97] 116.068221 1.814546619 115.7858077 3.2460162 32.352943 82.236391 160.723125 420.855401 4071.6871 0.9994627
times_uncensored_sampled[98] 112.737374 1.816119395 114.3306297 2.7398460 31.941124 76.296925 156.120253 410.530970 3963.1125 0.9995505
[ reached getOption("max.print") -- omitted 678 rows ]
exp_surv_model_draws <- tidybayes::tidy_draws(exp_surv_model_fit)
exp_surv_model_draws